On 22/01/2013 05:50, RichD wrote: > I saw a news item about a new technique to draw CO2 from > the atmosphere. It's a chemical process, using amines, > which binds with the molecule, coated on a large structure, > in the shape of a honeycomb. > > According to the story, this maximizes surface area. > ok, mathematicians, which function gets optimized by a > honeycomb? What are the constraints and assumptions?
2D problem to *minimise* the surface area to occupy a given volume. Bees use it to make honeycomb with the least amount of wax.
It is not difficult to show that the angle between sides must be 120 degrees and that equal lengths minimise total length/area occupied.
They have the structure just about as wrong as it is possible to be unless the stuff they are making it out of is extremely precious.
The 3D problem to occupy volume with a foam of minimum surface area is far more interesting and gives rise to Plateau's laws of soap films. The Kelvin foam structure was optimal until fairly recently when Weare-Phelan discovered a 3% better solution using a pair of shapes. A whole new family has been found but as yet a proof of optimality eludes.